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Engage and inspire students to read and comprehend a variety of mathematical concepts with the Leveled Texts for Mathematics series. Each book in the series contains 15 topics that have been expertly leveled at four distinct reading levels. A practice problem follows each text passage to promote class discussion and allow for students to apply what they learned from the passage.

Although the reading levels have been differentiated, each passage, including the graphics, appears the same to students. The graphics also serve as much-needed visual support, especially for English language learners. This combination of leveling and graphics makes differentiating mathematics content quick and easy.

The Teacher Resource CD includes full-color versions of the texts and modifiable versions of each passage in a text format that teachers can further adapt for student needs. Leveled Texts for Mathematics is a great tool for motivating students of all readiness levels!

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Promote Content-Area Literacy for All Students

Full-color Teacher Resource CD

Leveled Texts for M

athem

atics: Fractions, D

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© Shell Education #50785—Leveled Texts for Mathematics: Fractions, Decimals, and Percents

Table of ContentsWhat Is Differentiation? ............................................................................................ 4How to Differentiate Using This Product ........................................................... 5General Information About the Student Populations ..................................... 6

Below-Grade-Level Students .......................................................................... 6English Language Learners ............................................................................. 6On-Grade-Level Students ................................................................................. 7Above-Grade-Level Students.......................................................................... 7

Strategies for Using the Leveled Texts ................................................................. 8Below-Grade-Level Students .......................................................................... 8English Language Learners ...........................................................................11Above-Grade-Level Students........................................................................14

How to Use This Product ........................................................................................16Readability Chart ...............................................................................................16Components of the Product ..........................................................................16Tips for Managing the Product .....................................................................18Correlation to Standards ................................................................................19

Leveled Texts ...............................................................................................................21What Is a Fraction? ............................................................................................21Fractions Have Their Place .............................................................................29Finding a Place for Decimals .........................................................................37Some Are More, Some Are Less ....................................................................45Different but the Same ....................................................................................53As Simple as Possible .......................................................................................61When It’s Greater Than One ...........................................................................69Together or Apart ..............................................................................................77Thinking About Different Sizes ....................................................................85Multiplication and Division of Fractions ...................................................93Addition and Subtraction of Decimals ................................................... 101Multiplying and Dividing Decimals ......................................................... 109Fractions to Decimals ................................................................................... 117Understanding Percents .............................................................................. 125Fractions, Decimals, and Percents ............................................................ 133

Appendices ................................................................................................................. 141References Cited ............................................................................................. 141Contents of Teacher Resource CD ............................................................ 142

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#50785—Leveled Texts for Mathematics: Fractions, Decimals, and Percents © Shell Education

How to Use This Product

Readability Chart

Title of the Text

Star Circle Square TriangleWhat Is a Fraction? 2.2 3.0 5.3 6.6

Fractions Have Their Place 2.2 3.4 5.0 6.6

Finding a Place for Decimals 2.2 3.0 5.0 6.5

Some Are More, Some Are Less 1.9 3.0 5.0 6.5

Different but the Same 1.6 3.2 5.1 6.5

As Simple as Possible 2.2 3.2 5.1 6.6

When It's Greater Than One 2.2 3.5 5.1 6.6

Together or Apart 2.0 3.4 5.3 6.6

Thinking About Different Sizes 2.2 3.1 5.3 6.5

Multiplication and Division of Fractions 2.1 3.1 5.0 6.5

Addition and Subtraction of Decimals 2.2 3.2 5.2 6.5

Multiplying and Dividing Decimals 2.2 3.0 5.5 6.6

Fractions to Decimals 2.2 3.4 5.0 6.6

Understanding Percents 2.2 3.4 5.0 6.5

Fractions, Decimals, and Percents 2.2 3.4 5.0 6.5

Components of the Product

Strong Image Support• Each level of text includes important visual support. These images, diagrams,

photographs, and illustrations add interest to the texts and help students comprehend the mathematical concepts. The images also serve as visual support for second-language learners. They make the texts more context-rich and bring the examples to life.

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© Shell Education #50785—Leveled Texts for Mathematics: Fractions, Decimals, and Percents© Shell Education #50785—Leveled Texts for Mathematics: Fractions, Decimals, and Percents

What Is a Fraction? You know the word fraction. Do you know

where it comes from? It has the root fract-. That means “break.” The suffix -tion means “the result of.” The word fraction means “the result of breaking.” That makes sense. A fraction is a part of a whole.

Basic FactsA fraction is a number. It compares a part with a whole. It compares the number

of equal parts with the number in a whole. It can also be used to compare groups. A fraction can compare the number of equal groups with the total number of equal groups.

See the circle (right). It is split into two equal parts. One out of the two parts is shaded.We write “ 1

2 ” to show the number of shaded pieces. We say “one-half.”

These circles are split into two equal groups.One out of the two groups is shaded.We write “ 1

2 ” to show the number of shaded groups.We say “one-half.”

A fraction has two numbers. One is a numerator. The other is a denominator. The numerator tells you the number of equal parts. The denominator tells you the number parts in the whole. Look at the fraction 1

2 . The 1 is the numerator. The 2 is the denominator.

One-half Not one-half

Some numbers are made of a whole number and a fraction. Those are mixed numbers. Below, two whole rectangles are shaded. One-half of another rectangle is shaded. That means 2 1

2 rectangles are shaded.

2 12 is a mixed number.

2121


Examples of Fractions

See below. 14 (one-fourth) of the picture is shaded. 3

4 (three-fourths) is not. The 4 is the denominator. Each example is broken into four equal parts.

See below. 26

(two-sixths) of the picture is shaded. The 2 is the numerator. Each example has two equal parts shaded.

See below. 46

(four-sixths) of the picture is not shaded. The 4 is the numerator. Each example has four equal parts that are not shaded.

Fractions in Our Daily LivesThink of measuring cups. They come in

14 , 1

3 , 12 , 2

3 , 34 , and 1-cup sizes. Fractions are

used in recipes. Maybe one and one-half cups of flour are needed. Maybe three-fourths of a cup of sugar is needed. In cooking, fractions are needed.

You Try ItWhat fraction of the cookies is shaded?

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What Is a Fraction? You know the word fraction. Do you know

where it comes from? It has the Latin root fract-. That means “break.” The suffix -tion means “the result of.” So the word fraction means the “result of breaking.” That makes sense. A fraction is a part of a whole.

Basic FactsA fraction is a number. It compares a part with a whole. It compares a number

of equal parts with the number of parts in a whole. It can also compare groups. A fraction can compare the number of groups being used with the total number of groups.

The top circle (right) is split into two equal parts.One out of the two parts is shaded.We write “ 1


The circles are split into two equal groups.One out of the two groups is shaded.We write “ 1


A fraction has two numbers. One is a numerator. The other is a denominator. The numerator tells you the number of equal parts. The denominator tells you the number of equal parts in the whole. In the fraction 1

2 , the 1 is the numerator. The 2 is the denominator.


Some numbers are made of a whole number and a fraction. Those are mixed numbers. Below, we have two whole rectangles shaded. One-half of another rectangle is shaded. That means that 2 1



23


Examples of FractionsIn each case below, 1

4 (one-fourth) of the picture is shaded; 34 (three-fourths) is

not. The 4 is the denominator, since each example is broken into four equal parts.

In each case below, 26

(two-sixths) of the picture is shaded. The 2 is the numerator, since each example has two equal parts shaded.


(four-sixths) of the picture is not shaded. The 4 is the numerator, since each example has four equal parts that are not shaded.

Fractions in Our Daily LivesDo you have a set of measuring cups? They

come in 14 , 1

3 , 12 , 2

3 , 34 , and 1-cup sizes. This

is because fractions are used often in recipes. Maybe one and one-half cups of flour are needed, or three-fourths cup of sugar is called for. Whether cooking for two or 200, fractions are needed.


24


What Is a Fraction? Did you know that the word fraction comes

from the Latin root fract-, meaning “break?” The suffix -tion means “the result of.” So the word fraction means “the result of breaking.” That makes sense, since a fraction is a part of a whole.

Basic FactsA fraction is a number that compares a part with a whole. A fraction compares

the number of equal parts being used with the number of equal parts that make up a whole amount, or the number of equal groups being used with the total number of equal groups.

The circle at right is split into two equal parts.One out of the two parts is shaded.We write “ 1


The circles are split into two equal groups.One out of the two groups is shaded.We write “ 1


A fraction is made up of two numbers. One is a numerator. The other is a denominator. The numerator tells you the number of equal parts being used. The denominator tells you the number of equal parts that make up the whole. You looked at the fraction 1

2 . The 1 is the numerator. The 2 is the denominator.


Some numbers are made of a whole number and a fraction. Those are mixed numbers. Below, we have two whole rectangles shaded. One-half of another rectangle is shaded. That means that 2 1



25



4 (one-fourth) of the picture is shaded and 34 (three-fourths) is

not. The 4 is the denominator because each example is broken into four equal parts.


(two-sixths) of the picture is shaded. The 2 is the numerator because each example has two equal parts shaded.


(four-sixths) of the picture is not shaded. The 4 is the numerator because each example has four equal parts that are not shaded.

Fractions in Our Daily LivesHave you ever looked at a set of measuring

cups? Typically, they come in 14 , 1

3 , 12 , 2

3 , 34 ,

and 1-cup sizes. This is because fractions are used quite often when following recipes. Maybe one and one-half cups of flour are needed, or three-fourths cup of sugar is called for. Whether cooking for two or two hundred, fractions are needed.


26


What Is a Fraction? The word fraction is interesting. It comes

from two Latin roots: fract-, meaning “break,” and the suffix -tion, meaning “the result of.” So the word fraction literally means, “the result of breaking,” which makes sense, since a fraction compares a part to a whole.

Basic FactsA fraction compares two things: the number of equal parts being used, and the

number of equal parts that make up the whole amount. Or, it compares the number of equal groups being looked at and the total number of equal groups in all.

Look at this circle: it is split into two equal parts.One out of the two parts is shaded.Write “ 1

2 ” to represent the number of shaded pieces. We would say “one-half.”

These circles are split into two equal groups.One out of the two groups is shaded.Write “ 1

2 ” to represent the number of shaded groups.We would say “one-half.”

Within a fraction, you’ll see two numbers: a numerator and a denominator. The numerator tells you the number of equal parts being used. The denominator represents the total number of equal parts that make up the whole. If you looked at the fraction 1

2 , the 1 is the numerator and the 2 is the denominator.


Some numbers consist of a combination of a whole number and a fraction. Those are mixed numbers. For example, see how the two whole rectangles below are shaded. One-half of another rectangle has also been shaded. That means that 2 1

2 rectangles in all are shaded, which is a representation of a mixed number.


27



4 (one-fourth) of the picture is shaded, while 34 (three-fourths)

is not shaded. We use 4 as the denominator because each figure is broken into four equal parts.


(two-sixths) of the picture is shaded. The 2 is the numerator because each example has two equal parts shaded.


(four-sixths) of the picture is not shaded. The 4 is the numerator because each example has four equal parts that are not shaded.

Fractions in Our Daily LivesHave you ever carefully examined a set of

measuring cups? They are useful tools, because they measure ingredients in increments, typically 14 , 1

3 , 12 , 2

3 , 34 , and 1-cup at a time. This

is because when following recipes, we rely on fractions for exact amounts. A recipe may call for one and one-half cups of flour, or three-fourths cup of another ingredient. Regardless of how many you are cooking for, it is guaranteed that your recipe will call for fractional measurements.


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